Mathematics Problem solving

Test 3

 

  1. (a) A graph of the function is given below

Fill in the following table with approximate values (if they exist)

2 4 6 8 10 12 14
             

(b) For the function

find  and an equation of the tangent line to

the graph of the above function at

 

 

 

 

In the questions c to h , find

(C )

 

 

 

(d) You may use

 

(e)

 

 

 

 

 

 

 

(f)

 

 

 

 

 

 

(g) (2Find  if

i.e.

 

 

(2) (a) Find an equation of the tangent line to the graph of

at

 

Use geogebra or any other tool to draw a graph

of  and that of the tangent line to the graph of

at in the same window.

 

 

 

 

 

 

(b) Find an equation to the tangent line to the graph of

at

Use geogebra or any other tool to draw a graph

of  and that of the tangent line to the graph of  at

in the same window.

 

 

 

 

 

(c)    We are given the graphs of  and  below. Find , i.e. the derivative of  at 1.

 

 

 

 

 

(d) Find the differential of  . Find  , an equation of the tangent line to the graph of  at

 

 

 

 

 

  1. Two cars start moving from the same point. One travels east at a constant rate of 60 miles per hour and the other travels north at a constant rate of 70 miles per hour. Find the rate at which the distance between the cars is changing 1 hour later. You may round your answer to two digits after the decimal sign.

 

 

 

 

 

 

 

 

 

(e) Find    if  and find an equation of the tangent line to the graph of  at

 

 

 

 

 

(f) Find an equation of the tangent line to the graph of

 

at

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(g) Use Newton’s method to find the solution of

by using the following steps

(i) Find,  where

(ii) Find,  where

(iii) Choose a guess point

(iv) Perform the iterations, until the values stabilize to the 8-dgits after the decimal sign.

 

 

Last Updated on